Overall survival prediction for high-grade glioma patients using mathematical modeling of tumor cell infiltration

PURPOSE

This study aimed at applying a mathematical framework for the prediction of high-grade gliomas (HGGs) cell invasion into normal tissues for guiding the clinical target delineation, and at investigating the possibility of using tumor infiltration maps for patient overall survival (OS) prediction.

MATERIAL & METHODS

A model describing tumor infiltration into normal tissue was applied to 93 HGG cases. Tumor infiltration maps and corresponding isocontours with different cell densities were produced. ROC curves were used to seek correlations between the patient OS and the volume encompassed by a particular isocontour. Area-Under-the-Curve (AUC) values were used to determine the isocontour having the highest predictive ability. The optimal cut-off volume, having the highest sensitivity and specificity, for each isocontour was used to divide the patients in two groups for a Kaplan-Meier survival analysis.

RESULTS

The highest AUC value was obtained for the isocontour of cell densities 1000 cells/mm3 and 2000 cells/mm3, equal to 0.77 (p < 0.05). Correlation with the GTV yielded an AUC of 0.73 (p < 0.05). The Kaplan-Meier survival analysis using the 1000 cells/mm3 isocontour and the ROC optimal cut-off volume for patient group selection rendered a hazard ratio (HR) of 2.7 (p < 0.05), while the GTV rendered a HR = 1.6 (p < 0.05).

CONCLUSION

The simulated tumor cell invasion is a stronger predictor of overall survival than the segmented GTV, indicating the importance of using mathematical models for cell invasion to assist in the definition of the target for HGG patients.

Self-assembly of mesoscale collagen architectures and applications in 3D cell migration

3D in vitro tumor models have recently been investigated as they can recapitulate key features in the tumor microenvironment. Reconstruction of a biomimetic scaffold is critical in these models. However, most current methods focus on modulating local properties, e.g. micro- and nano-scaled topographies, without capturing the global millimeter or intermediate mesoscale features. Here we introduced a method for modulating the collagen I-based extracellular matrix structure by disruption of fibrillogenesis and the gelation process through mechanical agitation. With this method, we generated collagen scaffolds that are thickened and wavy at a larger scale while featuring global softness. Thickened collagen patches were interconnected with loose collagen networks, highly resembling collagen architecture in the tumor stroma. This thickened collagen network promoted tumor cell dissemination. In addition, this novel modified scaffold triggered differences in morphology and migratory behaviors of tumor cells. Altogether, our method for altered collagen architecture paves new ways for studying in detail cell behavior in physiologically relevant biological processes. STATEMENT OF SIGNIFICANCE: Tumor progression usually involves chronic tissue damage and repair processes. Hallmarks of tumors are highly overlapped with those of wound healing. To mimic the tumor milieu, collagen-based scaffolds are widely used. These scaffolds focus on modulating microscale topographies and mechanics, lacking global architecture similarity compared with in vivo architecture. Here we introduced one type of thick collagen bundles that mimics ECM architecture in human skin scars. These thickened collagen bundles are long and wavy while featuring global softness. This collagen architecture imposes fewer steric restraints and promotes tumor cell dissemination. Our findings demonstrate a distinct picture of cell behaviors and intercellular interactions, highlighting the importance of collagen architecture and spatial heterogeneity of the tumor microenvironment.

Learn-Morph-Infer: A new way of solving the inverse problem for brain tumor modeling

Current treatment planning of patients diagnosed with a brain tumor, such as glioma, could significantly benefit by accessing the spatial distribution of tumor cell concentration. Existing diagnostic modalities, e.g. magnetic resonance imaging (MRI), contrast sufficiently well areas of high cell density. In gliomas, however, they do not portray areas of low cell concentration, which can often serve as a source for the secondary appearance of the tumor after treatment. To estimate tumor cell densities beyond the visible boundaries of the lesion, numerical simulations of tumor growth could complement imaging information by providing estimates of full spatial distributions of tumor cells. Over recent years a corpus of literature on medical image-based tumor modeling was published. It includes different mathematical formalisms describing the forward tumor growth model. Alongside, various parametric inference schemes were developed to perform an efficient tumor model personalization, i.e. solving the inverse problem. However, the unifying drawback of all existing approaches is the time complexity of the model personalization which prohibits a potential integration of the modeling into clinical settings. In this work, we introduce a deep learning based methodology for inferring the patient-specific spatial distribution of brain tumors from T1Gd and FLAIR MRI medical scans. Coined as Learn-Morph-Infer, the method achieves real-time performance in the order of minutes on widely available hardware and the compute time is stable across tumor models of different complexity, such as reaction-diffusion and reaction-advection-diffusion models. We believe the proposed inverse solution approach not only bridges the way for clinical translation of brain tumor personalization but can also be adopted to other scientific and engineering domains.

The effects of exterior boundary conditions on a internally heated tumor tissue with a thermoporoelastic model

Modeling flow field in tumor regions interstitial space is of primary importance, because of the importance of advection in macromolecule drug delivery. Its deformation has also to be taken into account because of the forces caused by the fluid; if the tumor region is not isothermal, this deformation can be also strongly affected by temperature fields. In this paper, the effects of thermal boundary conditions on a tumor region periphery with an internal heat source are investigated. The tumor region is modeled as a deformable sphere, in which two phases can be distinguished. The fluid phase is the interstitial fluid, while the rest of the tumor is modeled as the solid phase, including also capillaries and tissues. Transient-state governing equations for mass, momentum and energy are written for both phases, by also considering tumor deformation under the linear elastic material assumption. A situation of Tumor Blood Flow (TBF) rapid decay, in which vascular pressure rapidly approaches to zero, is considered, while the heat source is modeled as a fourth-grade radial-decay function. Boundary conditions for the energy equation are varied on the external surface of the sphere, in order to appreciate the effects of the surrounding on flow and temperature fields inside the tumor. After scaling equations, a finite-element scheme is employed for the numerical solution. Comparisons with analytical solutions from literature show a good agreement. Results are shown for different dimensionless parameters that are referred to temperature, volumetric strain, pressure and velocity, showing in which case external boundary conditions strongly affect tumor region flow fields and a third-kind boundary condition is needed.

Three-Dimensional Modeling of Avascular Tumor Growth in Both Static and Dynamic Culture Platforms

Microfluidic cell culture platforms are ideal candidates for modeling the native tumor microenvironment because they can precisely reconstruct in vivo cellular behavior. Moreover, mathematical modeling of tumor growth can pave the way toward description and prediction of growth pattern as well as improving cancer treatment. In this study, a modified mathematical model based on concentration distribution is applied to tumor growth in both conventional static culture and dynamic microfluidic cell culture systems. Apoptosis and necrosis mechanisms are considered as the main inhibitory factors in the model, while tumor growth rate and nutrient consumption rate are modified in both quiescent and proliferative zones. We show that such modification can better predict the experimental results of tumor growth reported in the literature. Using numerical simulations, the effects of the concentrations of the nutrients as well as the initial tumor radius on the tumor growth are investigated and discussed. Furthermore, tumor growth is simulated by taking into account the dynamic perfusion into the proposed model. Subsequently, tumor growth kinetics in a three-dimensional (3D) microfluidic device containing a U-shaped barrier is numerically studied. For this case, the effect of the flow rate of culture medium on tumor growth is investigated as well. Finally, to evaluate the impact of the trap geometry on the tumor growth, a comparison is made between the tumor growth kinetics in two frequently used traps in microfluidic cell culture systems, i.e., the U-shaped barrier and microwell structures. The proposed model can provide insight into better predicting the growth and development of avascular tumor in both static and dynamic cell culture platforms.

Native-mimicking in vitro microenvironment: an elusive and seductive future for tumor modeling and tissue engineering

Human connective tissues are complex physiological microenvironments favorable for optimal survival, function, growth, proliferation, differentiation, migration, and death of tissue cells. Mimicking native tissue microenvironment using various three-dimensional (3D) tissue culture systems in vitro has been explored for decades, with great advances being achieved recently at material, design and application levels. These achievements are based on improved understandings about the functionalities of various tissue cells, the biocompatibility and biodegradability of scaffolding materials, the biologically functional factors within native tissues, and the pathophysiological conditions of native tissue microenvironments. Here we discuss these continuously evolving physical aspects of tissue microenvironment important for human disease modeling, with a focus on tumors, as well as for tissue repair and regeneration. The combined information about human tissue spaces reflects the necessities of considerations when configuring spatial microenvironments in vitro with native fidelity to culture cells and regenerate tissues that are beyond the formats of 2D and 3D cultures. It is important to associate tissue-specific cells with specific tissues and microenvironments therein for a better understanding of human biology and disease conditions and for the development of novel approaches to treat human diseases.

Hydrogels to model 3D in vitro microenvironment of tumor vascularization

A growing number of failing clinical trials for cancer therapy are substantiating the need to upgrade the current practice in culturing tumor cells and modeling tumor angiogenesis in vitro. Many attempts have been made to engineer vasculature in vitro by utilizing hydrogels, but the application of these tools in simulating in vivo tumor angiogenesis is still very new. In this review, we explore current use of hydrogels and their design parameters to engineer vasculogenesis and angiogenesis and to evaluate the angiogenic capability of cancerous cells and tissues. By coupling these hydrogels with other technologies such as lithography and three-dimensional printing, one can create an advanced microvessel model as microfluidic channels to more accurately capture the native angiogenesis process.